Analysis of Newly Designed Airfoil for Micro-Capacity Wind Turbine using Qbla...
Comparative Study of Yaw and Nacelle Tilt Control for a Two-Bladed Downwind Wind Turbine
1. Comparative Study of Yaw and Nacelle Tilt Control for a
Two-Bladed Downwind Wind Turbine
ABSTRACT
The structural dynamics and response of a two-bladed 16 RPM downwind wind turbine configuration based
on the model NREL 5MW offshore horizontal axis wind turbine (HAWT) is examined using Computational
Structural Dynamics (CSD) analysis. Nacelle tilt angles of 5, 20, 35, 50, and 65 degrees were investigated based
on various wind speeds in order to achieve same power output of 5 MW. Yaw angles of 20, 30, 40, 50, and 60
degrees were examined as well. This paper focuses on comparing various loads and displacements between the
two control methods. The computed load effects revealed that the tower top and base shear forces dropped
significantly using the nacelle tilt control compared to yaw control.
1. Introduction
Over the past few decades there has been a subnational increase in the usage and extraction of wind energy. This
trend is most likely to grow in the future. The necessity for improved cost effectiveness of wind power plants has
motivated growth in wind turbines’ size and rated power, thus increasing the structural load and fatigue that wind
turbines have to endure. However, the construction and maintenance of large wind turbines is very costly.
Wind turbines are designed to extract kinetic energy from the wind, usually to drive an electric generator. Almost
all of the commercial wind turbines today are horizontal axis wind turbines (HAWT), meaning that the axis of rotation
of the turbine rotor is horizontal. Two variations of this kind of wind turbine orientations are the upwind and downwind
configurations. This paper focuses solely on the downwind configuration. Downwind wind turbines do not typically
need a yaw control mechanism if the rotor and nacelle have a suitable design to make the nacelle passively align with
the wind. A significant advantage of the downwind wind turbine is that the rotor blades can be more flexible,
decreasing the weight of the whole rotor. The blades may bend at high wind speeds and reduce the load passed to the
tower. On the other hand, the disadvantage of the downwind wind turbine is the tower wake effect. The pressure
fluctuations on the turbine as the rotor passes through the tower shadow may cause a higher fatigue load on the turbine.
The two-bladed design is relatively easy to transport and may not require on-site assembly, thus lowering the cost.
The downside of offshore wind turbines compared to onshore is that installing and maintaining them is more
expensive.
In the present study, numerical investigations of the National Renewable Energy Laboratory 5MW reference wind
turbine is carried out for a downwind two-bladed 16 RPM configuration, in order to assess its aeromechanical
performance and structural response for offshore wind turbine applications. This study mainly focuses on the structural
dynamics of the particular configuration. The purpose of the current work is conduct low fidelity computational
simulation and analysis of two-bladed downwind turbine in order to assess the feasibility of this innovative wind
turbine control concepts. The Computational Structural Dynamics (CSD) solver DYMORE [2] was employed to study
the aerodynamic and structural performance on the rotor, the tower, and the impact of wind turbine wakes.
2. 2. Computational Method
The CSD code DYMORE-2 was developed at the Georgia Institute of Technology under the guidance of Dr.
Olivier Bauchau [3]. DYMORE models physical structures in the forms of beams, springs, cables, and other elements
in its finite element library, and treats nonlinear geometrical effects exactly. The structural element library in
DYMORE-2 is adequate to model complex geometries, such as wind turbines and helicopter rotors. DYMORE uses
the lifting line method, the 2-D look-up table of static aerodynamic characteristics, and dynamic inflow wake model
to perform the aerodynamics computations. The trim procedure based on the autopilot method is utilized and described
in [3]. A pseudo-time stepping method is employed within each simulation time step to converge the system. The
convergence criterion used here was the Energy-Like method, wherein the energy error of the solution was required
to be less than a specified percentage of the total system energy before each time step result was accepted. In this
version, DYMORE-2 employs an energy-decay scheme [4] to ensure the convergence in the process of structural
dynamics calculations.
3. Geometry and Model Setup
4.1 NREL 5MW Wind Turbine
The NREL offshore 5MW baseline wind turbine [1] is a conventional three-bladed upwind variable-speed,
variable blade-pitch-to-feather-controlled turbine, which is used as the reference for the computational study of the
two-bladed downwind configurations with innovative tilt control. Figure 1 shows the two-bladed downwind wind
turbine configurations at various nacelle tilt angles. The bottom blade is pointing to the ground in the z direction,
which is denoted as blade one at zero degrees azimuth. The wind turbine rotor blade has a radius of 63 meters. The
rotor has 2.5-degree pre-coning angle and 5-degree shaft tilt angle. The wind turbine blade is composed of eight
aerodynamic shapes including six airfoils and 2 cylinders with 13.3 degrees twist angle, as shown in Figure 2. The
detailed distribution of the airfoils, associated chord lengths, and aero-twist angles along the blade span direction can
be found in [1]. The tower height is 87.6 meter, with the top and base diameter of 3.87 and 6 meters, respectively.
Figure 1 Configurations of downwind wind turbines with various nacelle tilt angles
3. Figure 2 Wind turbine blade shape with sketch view
4.2 CSD Model Setup
Based on the physical wind turbine geometry and flow conditions of interests, deflections and structural loadings
are computed using DYMORE-2 in order to study the presence of system resonance, fatigue contributors, and the part
physical interference. CSD models constructed in this work include all structural properties of wind turbines and an
aerodynamic interface for accepting airloads computed by an external source. All models are set up according to the
NREL 5MW report [1], where a three-bladed upwind turbine was defined. The downwind two-bladed cases was set
up similar to the upwind three-bladed case. Blade pitch was set to zero-degree collective at 75% blade radius. The
performance of this configuration was predicted at the design operating conditions, and with no base motion.
Figure 3 illustrates the topology of the two-bladed CSD wind turbine model. The tower and blades were all
modeled as beams and meshed with 10 third-order finite elements, which are the main subjects of the computational
analysis. Other important features in the system performance are the yaw mechanism (modeled as a spring/damper
joint attaching the tower to the nacelle), the shaft (also a spring/damper element between the rotation joint and the
main revolving joint), and the concentrated mass which is on the opposite side of the yaw joint from the blade assembly
to represent the weight of the generator.
Figure 3 Wind turbine CSD model topology
The only difference in the CSD model topology between the NREL three-bladed configuration and the two-bladed
is the number of blades [1], and a teetering joint which was added to the two-bladed wind. Two-bladed wind turbines
generally have a teetering hub which mitigates the fluctuating loads, and lowers the fatigue damage in the drive train.
Another advantage of the teetering hub includes the reduction of uneven loads on the blades due to tower shadow [6].
There is a minor difference in mass between the rigid hub of the three-bladed wind turbine and the teetering hub of
4. the two-bladed wind turbine. This difference in mass will be neglected for the purposes of this study. Table 2 shows
the structure lumped parameter properties of the wind turbine.
Table 2 – Structure lumped parameter properties taken from Jonkman et al. [1]
Property Value
Blade Mass (kg) 17,740
Rotor Mass, 2bld (kg) 35,480
Nacelle Counter-weight mass (kg) 240,000
Hub Mass (kg) 58,780
Yaw mechanism stiffness / damping 9.028x109
N-m/rad 19.160x106
N-m/rad/s
Shaft stiffness / damping 867.6x106
N-m/rad 6.215x106
N-m/rad/s
All wind turbine configurations used the same spring and mass values and locations, and were different only in
the blade position relative to the tower and the number of blades. Concentrated mass and spring parameters were held
constant for all cases for the purpose of comparing the dynamic behavior among them. The static condition of the
wind turbine leaves a tower bending moment because of the nacelle weight distribution that tends to pitch the tower-
top assembly rotor-side-down. In all cases the rotor spin vector pointed into the incoming flow. Rotation of the main
rotor revolving joint was specified and then transferred to the blades so that the simulated shaft twist is in the direction
opposite of what happens in the real situation when the rotation is driven by rotor torque. In addition to the mechanical
setup of the wind turbine, DYMORE-2 has an aerodynamic model using simplified airfoil look-up tables and lifting
line calculations to apply airloads to various parts of the structure. The tower has an aerodynamic interface in the
DYMORE-2 model with 36 airstations spanning the height.
4. Blade Fatigue
A main cause of wind turbine damage is fatigue damage. Wind turbine blades are exposed to wind loadings that
cause growing fatigue damage owing to the loading’s cyclic nature. Blade fatigue can occur at various locations around
the blade and take various forms, such as local buckling, adhesive failure and bolted joint failure [6]. In the present
study it was concluded that as the nacelle tilt angle increased, the variations in displacements and bending moments
grew immensely. These variations are a contributing factor to fatigue damage to the wind turbine. Predicting fatigue
damage can be challenging due to lack of knowledge of the dynamic behavior of wind turbines [7].
One of the most essential processes in the design and development of a wind turbine is the prediction and
evaluation of a turbines dynamic behavior. This understanding can be valuable in approximating the energetic
performance as well as assessing the structural and fatigue damage of the wind turbine. It is very crucial to detect
fatigue damage during the early stages. Nowadays, the manufacturing process of wind turbine blades is greatly
automated, and many complications have already been eradicated. But there are still critical areas which are not
feasible with prevalent inspection techniques [8].
5. For a downwind wind turbine configuration, the wind field behind the tower is very complex to understand,
consisting of turbulence and unsteady motion. The tower shadow with its turbulent unsteady vortices and mean
velocity deficit is the most challenging part of a downwind wind turbine rotor. The turbulent unsteady vortices result
in impetuous loading on the blades, which contribute considerably to the blade fatigue loading as they pass through
the tower influenced region [5]. Wind turbine blades, which are subjected to repeated bending may develop cracks,
eventually would lead to complete component failure. There are various loads that contribute to fatigue in wind
turbines. Such as steady loads from high wind speeds, periodic loads from rotations and gravity, fatigue loads from
variations in wind speed, and resonance induced loads from the vibrations of structures [9].
5. Post-processing Procedure
In this paper, four types of internal loads are considered and examined:
1. Shear forces
2. Axial forces
3. Bending moments
4. Torsional moments
The shear forces and bending moments are combined by taking the root mean squared (RMS) values in two
different non-axial directions. The locations of interest at which the internal loads are evaluated include:
1. Tower base
2. Tower top
3. Blade root
The out-of –plane displacements of the tower and blades are also evaluated at the top of the tower and the tip of
the blades. Other displacement results include the tower twist at the top, and blade angular changes at the blade tip.
6. Results and Discussion
Structural dynamic analysis was performed on the two-bladed 16 RPM downwind wind turbine for numerous
nacelle tilt angles of 5, 20, 35, 50, and 65 degrees, and yaw angles of 20, 30, 40, 50, and 60 degrees. The sectional
aerodynamic forces and moments were all generated from the CSD DYMORE-2 code. The maximum, minimum, and
average loads are shown and evaluated in this section. All results compare the load effects for both yaw and tilt control
methods.
6.1 Tower Base
The towers and joints, being completely identical are considered first. The magnitude and unsteadiness of the
tower displacement, as well as the primary bending moment to the base of the tower reveals differences in the fatigue-
inducing loads to the tower. The load effects at the tower base are shown in Figure 4.
8. As shown in the plots above, the shear forces at the tower base drop significantly at increasing nacelle tilt angles
compared to yaw control method. The average shear force decreased by 64% at nacelle tilt of 65 degrees compared
to 5 degrees. But the downside is that the variance continues to increase as at higher nacelle tilt angles. This variance
can affect the performance of the overall wind turbine in the long run. The axial force also shows favorable results
for the nacelle tilt, as it continues to decrease at higher tilt angles. The bending moments for both control methods
show a similar trend, but the overall variance is slightly higher for the nacelle tilt control method. Additionally, the
torsional moment results are similar.
6.2 Tower Top
0
100
200
300
400
500
600
700
5
Degrees
Tilt
20
Degrees
Tilt
35
Degrees
Tilt
50
Degrees
Tilt
65
Degrees
Tilt
TowerTopShearForce(kN)
Maximum Average Minimum
0
100
200
300
400
500
600
700
20
Degrees
Yaw
30
Degrees
Yaw
40
Degrees
Yaw
50
Degrees
Yaw
60
Degrees
Yaw
TowerTopShearForce(kN)
Maximum Average Minimum
-3500
-3400
-3300
-3200
-3100
-3000
-2900
-2800
-2700
5
Degrees
Tilt
20
Degrees
Tilt
35
Degrees
Tilt
50
Degrees
Tilt
65
Degrees
Tilt
TowerTopAxialForce(kN)
Maximum Average Minimum
-3500
-3400
-3300
-3200
-3100
-3000
-2900
-2800
-2700
20
Degrees
Yaw
30
Degrees
Yaw
40
Degrees
Yaw
50
Degrees
Yaw
60
Degrees
Yaw
TowerTopAxialForce(kN)
Maximum Average Minimum
10. The load effects shown at the top of the tower are quite similar to those at the tower base, as shown in Figure 5.
However, the bending moments show dissimilar outcomes when comparing both locations. The average values of
the bending moments for all yaw angles is constant, unlike at the tower base where it slightly decreased.
Furthermore, the average values of the bending moments gradually decrease at increasing nacelle tilt angles, but this
time the direction of the bending moment at 65 nacelle tilt changes direction.
6.3 Blade Root
Blade root is an ideal point of interest to evaluate the load effects on the wind turbine. Figure 6 shows the load
effects at the blade roots.
0
50
100
150
200
250
300
350
400
450
500
5
Degrees
Tilt
20
Degrees
Tilt
35
Degrees
Tlt
50
Degrees
Tilt
65
Degrees
Tilt
BladeRootShearForce(kN)
Maximum Average Minimum
0
50
100
150
200
250
300
350
400
450
500
20
Degrees
Yaw
30
Degrees
Yaw
40
Degrees
Yaw
50
Degrees
Yaw
60
Degrees
Yaw
BladeRootShearForce(kN)
Maximum Average Minimum
0
200
400
600
800
1000
1200
1400
5
Degrees
Tilt
20
Degrees
Tilt
35
Degrees
Tlt
50
Degrees
Tilt
65
Degrees
Tilt
BladeRootAxialForce(kN)
Maximum Average Minimum
0
200
400
600
800
1000
1200
1400
20
Degrees
Yaw
30
Degrees
Yaw
40
Degrees
Yaw
50
Degrees
Yaw
60
Degrees
Yaw
BladeRootAxialForce(kN)
Maximum Average Minimum
12. The load effects shown in Figure 6 reveal minor changes in bending and torsional moments between the yaw
and nacelle tilt control methods. The axial forces for both control methods evaluated at all locations show constant
average values, with a slight favorable outcome for the nacelle tilt, as the variance in this case decreases with
increasing tilt angles. The biggest difference in results is the shear forces. Furthermore, the average values of the
shear forces remains constant at all yaw degrees, and the variance increases. This means the fluctuations in the shear
forces continues to increase at higher yaw angles but the average value remains constant. However, the same is not
true for nacelle tilt, as the average shear forces values continue to drop with increasing nacelle tilt angles.
6.4 Out-of-plane Displacements
Figure 7 shows the out-of-plane displacements at the blade tip and the tower top. Both control methods illustrate
similar displacement trends with no major differences.
Figure 7 Displacement effects at blade tip and tower top
0
2
4
6
8
10
12
5
Degrees
Tilt
20
Degrees
Tilt
35
Degrees
Tilt
50
Degrees
Tilt
65
Degrees
Tilt
Out-of-planeBladeTipDisplacement(m)
Maximum Average Minimum
0
2
4
6
8
10
12
20
Degrees
Yaw
30
Degrees
Yaw
40
Degrees
Yaw
50
Degrees
Yaw
60
Degrees
Yaw
Out-of-planeBladeTipDisplacement(m)
Maximum Average Minimum
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
5
Degrees
Tilt
20
Degrees
Tilt
35
Degrees
Tilt
50
Degrees
Tilt
65
Degrees
Tilt
Out-of-planeTowerTopDisplacement
(m)
Maximum Average Minimum
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
20
Degrees
Yaw
30
Degrees
Yaw
40
Degrees
Yaw
50
Degrees
Yaw
60
Degrees
Yaw
Out-of-planeTowerTipDisplacement
(m)
Maximum Average Minimum
13. 6.5 Blade Tip Angular Displacements
Blade angular displacement is another indicator of the degree to which aerodynamics would be affected by
deformation-based changes. Figure 8 shows these results.
Figure 8 Angular displacement effects at blade tip
6.6 Tower Top Angular Displacements
Figure 9 shows the tower top twist or angular displacements. The major difference seen between both control
systems is the direction of the displacements as they are slightly different.
Figure 9 Angular displacement effects at tower top
0
0.5
1
1.5
2
2.5
5
Degrees
Tilt
20
Degrees
Tilt
35
Degrees
Tilt
50
Degrees
Tilt
65
Degrees
Tilt
BladeTipAngularDisplacement(degrees)
Maximum Average Minimum
0
0.5
1
1.5
2
2.5
20
Degrees
Yaw
30
Degrees
Yaw
40
Degrees
Yaw
50
Degrees
Yaw
60
Degrees
Yaw
BladeTipAngularDisplacement(degrees)
Maximum Average Minimum
-0.32
-0.27
-0.22
-0.17
-0.12
-0.07
-0.02
0.03
0.08
5
Degrees
Tilt
20
Degrees
Tilt
35
Degrees
Tilt
50
Degrees
Tilt
65
Degrees
Tilt
TowerTopTwistDisplacement(degrees)
Maximum Average Minimum
-0.32
-0.27
-0.22
-0.17
-0.12
-0.07
-0.02
0.03
0.08
20
Degrees
Yaw
30
Degrees
Yaw
40
Degrees
Yaw
50
Degrees
Yaw
60
Degrees
Yaw
TowerTopTwistDisplacement(degrees)
Maximum Average Minimum
14. 6.7 Fatigue Load
In this research, there was no specific fatigue analysis done in order to determine its effect on the different
loadings. However, the shear forces and bending moments are the dominant components at the tower base, and the
shear forces cause the most damage at the tower top [10]. Based on this information and the results we obtained in
this paper, the nacelle tilt control method showed favorable outcomes when compared to the yaw control. The shear
forces and bending moments reduced significantly for nacelle tilt at tower base and top with comparison to yaw
control. This means the fatigue loading at 65 degrees tilt is lower than that at 5 degrees tilt. The same goes for the
bending moments, as it is the most dominant fatigue load at the tower base. Nacelle tilt results showed lower bending
moments at increasing tilt compared to yaw control.
7. Conclusion
In this research, the load effects on an NREL downwind wind turbine are compared. Two control methods are
employed in this study in order to determine which method is superior. The nacelle tilt control method revealed
favorable loading effects compared to the yaw control method. In terms of fatigue loadings, the shear forces and
bending moments had the most negative effect on the wind turbine. At higher nacelle tilt angles the fatigue loadings
decreased considerably compared to increasing yaw angles. In general, both control methods resulted in reduction of
loads at increasing yaw and nacelle tilt angles. However, nacelle tilt control revealed better results than yaw control.
8. References
[1] Jonkman, J., Butterfield, S., Musial, W., Scott, G., “Definition of a 5-MW Reference Wind Turbine for Offshore
System Development,” NREL Technical Report NREL/TP-500-38060, February 2009.
[2] Sheng, C., and Narramore, J.C., “Computational Simulation and Analysis of Bell Boeing Quad Tiltrotor Aero
Interaction,” Journal of the American Helicopter Society, Vol. 27, No. 4, October 2009, pp 1-15.
[3] Bauchau, O. A., DYMORE Users’ Manual, School of Aerospace Engineering, Georgia Institute of Technology,
Atlanta, Georgia, December 2006.
[4] Bauchau, O. A., “Computational Schemes for Flexible, Nonlinear Multi-Body Systems,” Multibody System
Dynamics, vol. 2, pp. 169-225, 1998.
[5] Marit Reiso, “The Tower Shadow Effect in Downwind Wind Turbines”, May 2013
[6] G. Freebury and W. Musial, “Determining Equivalent Damage Loading for Full-Scale Wind Turbine Blade
Fatigue Tests,” 19th
American Society of Mechanical Engineers (ASME) Wind Energy Symposium, 10-13 January
2010, Reno, Nevada.
[7] M. S. Rouabah and Z. L. Mahri, “Fatigue Estimation for a Rotating Blade of a Wind Turbine,” vol. 5, pp. 39-47,
2002
[8] Anne Jungert, “Damage Detection in Wind Turbine Blades using two Different Acoustic Techniques,” 7th
fib
PhD Symposium, 11-13, September, 2008
[9] Satishkumar V Tawade, Sachin B Todkar, Ashwinikumar S Hade, “FATIGUE LIFE OPTIMIZATION OF
WIND TURBINE BLADE,” International Journal of Research in Engineering and Technology
[10] Jin Woo Lee, Musarrat Jehan, Brett Anderson, Abdollah Afjeh, Efstratios Nikolaidis, “COMPARATIVE
STUDY OF TWO-BLADED UPWIND AND DOWNWIND TURBINES USING THE NREL REFERENCE
WIND TURBINE,” IMECE, 14-20, November, 2014
![Comparative Study of Yaw and Nacelle Tilt Control for a
Two-Bladed Downwind Wind Turbine
ABSTRACT
The structural dynamics and response of a two-bladed 16 RPM downwind wind turbine configuration based
on the model NREL 5MW offshore horizontal axis wind turbine (HAWT) is examined using Computational
Structural Dynamics (CSD) analysis. Nacelle tilt angles of 5, 20, 35, 50, and 65 degrees were investigated based
on various wind speeds in order to achieve same power output of 5 MW. Yaw angles of 20, 30, 40, 50, and 60
degrees were examined as well. This paper focuses on comparing various loads and displacements between the
two control methods. The computed load effects revealed that the tower top and base shear forces dropped
significantly using the nacelle tilt control compared to yaw control.
1. Introduction
Over the past few decades there has been a subnational increase in the usage and extraction of wind energy. This
trend is most likely to grow in the future. The necessity for improved cost effectiveness of wind power plants has
motivated growth in wind turbines’ size and rated power, thus increasing the structural load and fatigue that wind
turbines have to endure. However, the construction and maintenance of large wind turbines is very costly.
Wind turbines are designed to extract kinetic energy from the wind, usually to drive an electric generator. Almost
all of the commercial wind turbines today are horizontal axis wind turbines (HAWT), meaning that the axis of rotation
of the turbine rotor is horizontal. Two variations of this kind of wind turbine orientations are the upwind and downwind
configurations. This paper focuses solely on the downwind configuration. Downwind wind turbines do not typically
need a yaw control mechanism if the rotor and nacelle have a suitable design to make the nacelle passively align with
the wind. A significant advantage of the downwind wind turbine is that the rotor blades can be more flexible,
decreasing the weight of the whole rotor. The blades may bend at high wind speeds and reduce the load passed to the
tower. On the other hand, the disadvantage of the downwind wind turbine is the tower wake effect. The pressure
fluctuations on the turbine as the rotor passes through the tower shadow may cause a higher fatigue load on the turbine.
The two-bladed design is relatively easy to transport and may not require on-site assembly, thus lowering the cost.
The downside of offshore wind turbines compared to onshore is that installing and maintaining them is more
expensive.
In the present study, numerical investigations of the National Renewable Energy Laboratory 5MW reference wind
turbine is carried out for a downwind two-bladed 16 RPM configuration, in order to assess its aeromechanical
performance and structural response for offshore wind turbine applications. This study mainly focuses on the structural
dynamics of the particular configuration. The purpose of the current work is conduct low fidelity computational
simulation and analysis of two-bladed downwind turbine in order to assess the feasibility of this innovative wind
turbine control concepts. The Computational Structural Dynamics (CSD) solver DYMORE [2] was employed to study
the aerodynamic and structural performance on the rotor, the tower, and the impact of wind turbine wakes.](https://image.slidesharecdn.com/37cb2965-b623-4c4e-9a2b-cfa02e9cf80d-150824165812-lva1-app6892/85/comparative-study-of-yaw-and-nacelle-tilt-control-for-a-twobladed-downwind-wind-turbine-1-320.jpg)
![2. Computational Method
The CSD code DYMORE-2 was developed at the Georgia Institute of Technology under the guidance of Dr.
Olivier Bauchau [3]. DYMORE models physical structures in the forms of beams, springs, cables, and other elements
in its finite element library, and treats nonlinear geometrical effects exactly. The structural element library in
DYMORE-2 is adequate to model complex geometries, such as wind turbines and helicopter rotors. DYMORE uses
the lifting line method, the 2-D look-up table of static aerodynamic characteristics, and dynamic inflow wake model
to perform the aerodynamics computations. The trim procedure based on the autopilot method is utilized and described
in [3]. A pseudo-time stepping method is employed within each simulation time step to converge the system. The
convergence criterion used here was the Energy-Like method, wherein the energy error of the solution was required
to be less than a specified percentage of the total system energy before each time step result was accepted. In this
version, DYMORE-2 employs an energy-decay scheme [4] to ensure the convergence in the process of structural
dynamics calculations.
3. Geometry and Model Setup
4.1 NREL 5MW Wind Turbine
The NREL offshore 5MW baseline wind turbine [1] is a conventional three-bladed upwind variable-speed,
variable blade-pitch-to-feather-controlled turbine, which is used as the reference for the computational study of the
two-bladed downwind configurations with innovative tilt control. Figure 1 shows the two-bladed downwind wind
turbine configurations at various nacelle tilt angles. The bottom blade is pointing to the ground in the z direction,
which is denoted as blade one at zero degrees azimuth. The wind turbine rotor blade has a radius of 63 meters. The
rotor has 2.5-degree pre-coning angle and 5-degree shaft tilt angle. The wind turbine blade is composed of eight
aerodynamic shapes including six airfoils and 2 cylinders with 13.3 degrees twist angle, as shown in Figure 2. The
detailed distribution of the airfoils, associated chord lengths, and aero-twist angles along the blade span direction can
be found in [1]. The tower height is 87.6 meter, with the top and base diameter of 3.87 and 6 meters, respectively.
Figure 1 Configurations of downwind wind turbines with various nacelle tilt angles](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)